Numerical simulation of Czochralski crystal growth under the influence of a … (original) (raw)
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Journal of Crystal Growth, 2008
We present numerical simulations of vapor pressure controlled (VCz) and liquid encapsulated Czochralski (LEC) crystal growth of GaAs under the influence of a traveling magnetic field (TMF) with melt diameters of approximately 6 in and melt heights of approximately 1.8 in. The TMF is generated by an internal heater-magnet module (HMM) inside the pressure chamber in the growth arrangement and has been developed within the project KRIST g MAG, see http://www.kristmag.com. For the global simulation, i.e. for the computation in the entire pressure chamber, the software WIAS-HiTNIHS is used. We validate this software by comparing measured and simulated Lorentz forces. Furthermore, we discuss how to account for effects of nonaxisymmetric parts of the growth configuration during the axisymmetric computations performed by WIAS-HiTNIHS.
Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals
Crystal Research and Technology, 2003
The results of three-dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three-dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two-dimensional steady and three-dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three-dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.
Three-dimensional transient modeling of the melt flow in a TMF VCz system for GaAs crystal growth
Magnetohydrodynamics
Numerical modeling of electromagnetic, thermal and flow field is used to analyse the influence of a traveling magnetic field (TMF) applied during crystal growth of GaAs in a VCz crystal growth system. The TMF is generated by a heater-magnet module (HMM), combining the generation of heat and electromagnetic Lorentz forces. The influence of different electrical as well as geometrical parameters on the TMF effects have been investigated. The numerical results allow an optimal HMM design for the VCz system for growing GaAs and other semiconductor crystals.
3D computations of melt convection and crystallization front geometry during VCz GaAs growth
Journal of Crystal Growth, 2004
We have investigated the capabilities of modern numerical methods for the prediction of the melt/crystal interface geometry during encapsulated GaAs Czochralski growth with the vapor pressure control. Using an advanced Navier-Stokes solver, characteristics of 3D unsteady melt turbulent convection are studied for real growth regimes and the results are compared with the data by the conventional 2D steady approach. The effect of radiative heat exchange in the encapsulant is estimated with respect to its influence on the crystallization front geometry. The analysis is performed using experimental data for the growth of 3-and 4-inch GaAs crystals. r
Journal of Crystal Growth, 2005
We present a 2D model for the unsteady carbon transport and incorporation into the crystal during the vapor pressure-controlled Czochralski growth of semi-insulating GaAs. The model is based on a conjugated analysis of global heat transfer, turbulent melt convection, and the flow in the encapsulant within a quasi steady-state approximation. Carbon transport in the melt is coupled to the transport of carbon monoxide in B 2 O 3 encapsulant, assuming CO dissolution at the melt/encapsulant interface. CO concentration in the gas near the encapsulant surface, estimated from experimental observations, is used to formulate an external boundary condition. The model is validated using measurements of carbon concentration in grown 3-in GaAs crystals. The results obtained help to reveal basic mechanisms controlling carbon incorporation into the crystal. r
Crystal growth by a modified vapor pressure-controlled Czochralski (VCz) technique
Journal of Crystal Growth, 2008
A modified vapor pressure-controlled Czochralski (VCz) method is reported which employs a diving bell around the growing crystal. Semi-insulating (SI) GaAs crystals with a diameter of 160 mm and an overall length up to 220 mm were grown from melts of up to 23 kg, and compared with similar-sized crystals grown using a standard liquid-encapsulation Czochralski (LEC) process. Optimization of the VCz process was assisted by global numerical simulations. A slightly convex growth interface has been found to be the most suitable one for achieving a relatively low EPD of $10 4 cm À2 , with an associated reduction in the probability of dislocation bunching. The carbon concentration of the crystals was controlled down to values of 10 14 cm À3. The electrical properties, including the EL21 content are discussed.
Mathematical Modeling of Czochralski Type Growth Processes for Semiconductor Bulk Single Crystals
Milan Journal of Mathematics, 2012
This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e. g., silicon (Si) or gallium arsenide (GaAs) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.
Time-dependent magnetic field influence on GaAs crystal growth by vertical Bridgman method
Journal of Crystal Growth, 2004
The paper deals with the numerical investigation of time-dependent magnetic field influence on GaAs crystal growth by vertical Bridgman method. Fully unsteady numerical simulation is performed for three types of dynamic magnetic fields: rotating magnetic field (RMF), axial alternating magnetic field (AMF) and travelling magnetic field (TMF). The fields of stream function in the melt, temperature and dopant distribution in the melt and in the grown crystal with and without magnetic field are obtained and analyzed. RMF is found to pose significant influence on both azimuthal and meridional melt flows towards their intensification, and to substantially reduce the interface deflection. Higher magnetic field intensity results in the crystal-melt interface shape change from a concave interface to W-shaped one. At certain value of magnetic field intensity the steady-state flow regime becomes unstable and the transition to time-dependent regime is observed. The influence of AMF on GaAs crystal growth is found to be similar to that of static magnetic field. Application of travelling magnetic field significantly changes the flow structure, the interface shape and the dopant distribution in a melt and grown crystal. Depending on the propagation direction it can make either positive or negative effect on the resulting flow structure.